On noisy duplication channels with Markov sources

TL;DR

This paper extends information-theoretic results to noisy duplication channels modeled by ergodic Markov processes, establishing the asymptotic equipartition property and estimating channel capacities relevant to nanopore sequencing.

Contribution

It proves the AEP for noisy duplication processes based on ergodic Markov sources and relates it to hidden semi-Markov processes, advancing understanding of channel capacity.

Findings

Noisy duplication channel is information stable for ergodic Markov sources.

Lower bounds on capacity for binary symmetric channels with duplications are estimated.

The AEP for noisy duplication processes is related to that of hidden semi-Markov processes.

Abstract

Channels with noisy duplications have recently been used to model the nanopore sequencer. This paper extends some foundational information-theoretic results to this new scenario. We prove the asymptotic equipartition property (AEP) for noisy duplication processes based on ergodic Markov processes. A consequence is that the noisy duplication channel is information stable for ergodic Markov sources, and therefore the channel capacity constrained to Markov sources is the Markov-constrained Shannon capacity. We use the AEP to estimate lower bounds on the capacity of the binary symmetric channel with Bernoulli and geometric duplications using Monte Carlo simulations. In addition, we relate the AEP for noisy duplication processes to the AEP for hidden semi-Markov processes.